基于小波有限元与一阶Tikhonov正则化的移动车载识别研究
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摘要
车桥一直是交通工程的重要部分。在长期的车桥系统监测过程中发现，当移动车辆通过时，桥面所承受的移动载荷不能视为静态的；另一方面，对大跨度公路或铁路桥梁的实时荷载识别及其安全状态评估变得越来越重要和迫切。因此，对车桥系统中的移动载荷进行识别具有至关重要的意义。
本文对车桥系统中的车桥建模及移动载荷识别方法进行了研究，将文中提出的方法与传统的方法想比较，针对不同结构下的模型，分析在不同因素，例如噪声、测量参数、车桥系统参数的影响下，车桥模型及移动车载识别方法的可行性及准确性，为桥梁结构的安全评估及车辆超重监测，也为今后的桥梁设计等提供更为准确的依据。
本文的主要研究内容和取得的成果有：
（1）提出了一种新的车桥系统建模方法，即小波有限元法(WFEM)。该方法采用区间B样条小波尺度函数，通过转换矩阵使物理参数以小波系数的函数表达出来，从而将物理空间与小波空间关联，实现模型的小波参数化。利用该小波尺度函数的多尺度多分辨特性，模拟出模型的细节或框架特征，从而达到调节模型精度的目的。基于该模型的振动分析表明，与传统有限元方法(TFEM)相比，本文提出的车桥系统建模方法对单元数需求少且精度高，这对于提高大型或复杂结构模型的精度与分析效率具有重要意义。
（2）提出了一阶Tikhonov正则化技术与动态规划法相结合的移动载荷识别方法。首先对状态空间下的车桥系统运动方程进行离散，通过微小时间步长内各参数间的关系建立起待识别移动载荷与测得动响应之间的联系。采用动态规划法，通过迭代运算建立系统参数与优化变量之间的关系，对优化变量进行逆序与正序的反复迭代运算，最终获得最优的移动载荷。由于识别过程中的病态问题，借助L-曲线法选取最优正则化参数，并采用一阶Tikhonov正则化消除识别结果中的两端振荡现象、平滑噪声的影响。数值仿真结果表明，本文提出的一阶Tikhonov正则化与动态规划法相结合的识别方法，不仅能够平滑噪声，而且能够消除移动载荷进入及移出桥面时的两端振荡现象。
（3）对简支梁及连续梁桥模型上的移动车载进行识别。将本文提出的车桥系统建模方法与TFEM方法进行比较，说明本文建模方法的可行性及对大型结构的适用性。通过对比零阶Tikhonov正则化下的移动载荷识别结果说明一阶Tikhonov正则化与动态规划法识别移动载荷的优越性。同时，分析车桥模型中各种影响因素对移动载荷识别结果的影响。数值仿真结果表明采样频率、车速、测点数目及分布位置、车轴间距等对移动车载的识别结果都有一定程度的影响。
The vehicles and bridges are always one of the significant parts for traffic engineering. It iscrucial for vehicle-bridge system to identify the moving forces, not only because the interactionforces induced by vehicles couldn’t be simplified as static ones during the long time observation,but also because it is important and imperative to obtain the real-time moving forces on highwayand railway bridges for the safe estimation.
This dissertation studies the modeling methods for vehicle-bridge system and identificdationmethods for moving forces on the system. The new methods for modeling and for moving forceidentification are compared with traditional methods to validate the properties of feasibility andcorrectness for different structures, with different influence factors, such as noise level,measurement parameters, vehicle-bridge system parameters, et al. According to the analysis, it iscapable of more accurate design for bridges and of more accurate monitoring for moving vehicle.
The main contents of this dissertation are as follows:
（1）In Chapter2, a modeling method called wavelet finite elemtent method (WFEM) forvehicle bridge system is studied. To parameterize the model, the B Spline Wavlet in theInterval (BSWI) is adopted to connect the physical and wavelet spaces throughtransformation matrix by expressing the physical parameters with wavelet functions. Theprecision of the model is controlled by the multi-scale and multi-resolution property ofWFEM, through which both the detail and coarse characteristics can be obtained. Thevibration analysis is applied to validate that fewer elements are needed for WFEMmodel and the precision is satisfied compared with traditional finite element method(TFEM), which is meaningful for the improvement of precision and efficient of large orcomplicated structure.
（2）In Chapter3, a method for moving force identification based on the first order Tikhonov regularization and dynamic programming technique is studied. Fist, the relationshipbetween moving forces to be identified and the measured dynamic responses isestablished by the parameters in tiny time domain, which are discreted from the motionfunction in state space. Then, moving force is obtained using dynamic programmingtechnique by backward and forward iteration operation on optimal varialbes to gain theconnection of system parameters and optimal variables. The L-curve method isintroduced to find out the optimal parameter and the first order Tikhonov reguralizationis deduced for both smoothing the noise and avoiding the fluctuations when movingvehicles are moving in and out the bridge.
（3）In Chapter4, identification of moving forces on simply supported and continuousbridges is studied. First to validate the feasibility and the commonatity of the newmodeling method compared with TFEM, then to certificate the advantage of firstTikhonov regularization by the comparision of the identified results of moving forceswith the results under zero order Tikhonov regularization. The effects of parameters onidentification accuracy are analyzed, and the numerical simulation gives the conclusionthat the influence parameters such as the sampling frequency, the vehicle speed, thenumber and the arrangement of the measurement sensors, the axle spacing of vehicles, etal affect the accuracy of identified results to some extent.
本文对车桥系统中的车桥建模及移动载荷识别方法进行了研究，将文中提出的方法与传统的方法想比较，针对不同结构下的模型，分析在不同因素，例如噪声、测量参数、车桥系统参数的影响下，车桥模型及移动车载识别方法的可行性及准确性，为桥梁结构的安全评估及车辆超重监测，也为今后的桥梁设计等提供更为准确的依据。
本文的主要研究内容和取得的成果有：
（1）提出了一种新的车桥系统建模方法，即小波有限元法(WFEM)。该方法采用区间B样条小波尺度函数，通过转换矩阵使物理参数以小波系数的函数表达出来，从而将物理空间与小波空间关联，实现模型的小波参数化。利用该小波尺度函数的多尺度多分辨特性，模拟出模型的细节或框架特征，从而达到调节模型精度的目的。基于该模型的振动分析表明，与传统有限元方法(TFEM)相比，本文提出的车桥系统建模方法对单元数需求少且精度高，这对于提高大型或复杂结构模型的精度与分析效率具有重要意义。
（2）提出了一阶Tikhonov正则化技术与动态规划法相结合的移动载荷识别方法。首先对状态空间下的车桥系统运动方程进行离散，通过微小时间步长内各参数间的关系建立起待识别移动载荷与测得动响应之间的联系。采用动态规划法，通过迭代运算建立系统参数与优化变量之间的关系，对优化变量进行逆序与正序的反复迭代运算，最终获得最优的移动载荷。由于识别过程中的病态问题，借助L-曲线法选取最优正则化参数，并采用一阶Tikhonov正则化消除识别结果中的两端振荡现象、平滑噪声的影响。数值仿真结果表明，本文提出的一阶Tikhonov正则化与动态规划法相结合的识别方法，不仅能够平滑噪声，而且能够消除移动载荷进入及移出桥面时的两端振荡现象。
（3）对简支梁及连续梁桥模型上的移动车载进行识别。将本文提出的车桥系统建模方法与TFEM方法进行比较，说明本文建模方法的可行性及对大型结构的适用性。通过对比零阶Tikhonov正则化下的移动载荷识别结果说明一阶Tikhonov正则化与动态规划法识别移动载荷的优越性。同时，分析车桥模型中各种影响因素对移动载荷识别结果的影响。数值仿真结果表明采样频率、车速、测点数目及分布位置、车轴间距等对移动车载的识别结果都有一定程度的影响。
The vehicles and bridges are always one of the significant parts for traffic engineering. It iscrucial for vehicle-bridge system to identify the moving forces, not only because the interactionforces induced by vehicles couldn’t be simplified as static ones during the long time observation,but also because it is important and imperative to obtain the real-time moving forces on highwayand railway bridges for the safe estimation.
This dissertation studies the modeling methods for vehicle-bridge system and identificdationmethods for moving forces on the system. The new methods for modeling and for moving forceidentification are compared with traditional methods to validate the properties of feasibility andcorrectness for different structures, with different influence factors, such as noise level,measurement parameters, vehicle-bridge system parameters, et al. According to the analysis, it iscapable of more accurate design for bridges and of more accurate monitoring for moving vehicle.
The main contents of this dissertation are as follows:
（1）In Chapter2, a modeling method called wavelet finite elemtent method (WFEM) forvehicle bridge system is studied. To parameterize the model, the B Spline Wavlet in theInterval (BSWI) is adopted to connect the physical and wavelet spaces throughtransformation matrix by expressing the physical parameters with wavelet functions. Theprecision of the model is controlled by the multi-scale and multi-resolution property ofWFEM, through which both the detail and coarse characteristics can be obtained. Thevibration analysis is applied to validate that fewer elements are needed for WFEMmodel and the precision is satisfied compared with traditional finite element method(TFEM), which is meaningful for the improvement of precision and efficient of large orcomplicated structure.
（2）In Chapter3, a method for moving force identification based on the first order Tikhonov regularization and dynamic programming technique is studied. Fist, the relationshipbetween moving forces to be identified and the measured dynamic responses isestablished by the parameters in tiny time domain, which are discreted from the motionfunction in state space. Then, moving force is obtained using dynamic programmingtechnique by backward and forward iteration operation on optimal varialbes to gain theconnection of system parameters and optimal variables. The L-curve method isintroduced to find out the optimal parameter and the first order Tikhonov reguralizationis deduced for both smoothing the noise and avoiding the fluctuations when movingvehicles are moving in and out the bridge.
（3）In Chapter4, identification of moving forces on simply supported and continuousbridges is studied. First to validate the feasibility and the commonatity of the newmodeling method compared with TFEM, then to certificate the advantage of firstTikhonov regularization by the comparision of the identified results of moving forceswith the results under zero order Tikhonov regularization. The effects of parameters onidentification accuracy are analyzed, and the numerical simulation gives the conclusionthat the influence parameters such as the sampling frequency, the vehicle speed, thenumber and the arrangement of the measurement sensors, the axle spacing of vehicles, etal affect the accuracy of identified results to some extent.
引文
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